[commandlinefan]

> What about -3 * -2?

My son actually asked me that a while back (or rather, “why does a negative times a negative make a positive?”), and I honestly didn’t have a very satisfying answer. The best I could come up with was to go back to the definition of multiplication as repeated addition and then start with multiplying/repeated-adding a negative number by a positive number: that would work backward on the number line and give you a negative number. Then, since multiplication is commutative, a positive number multiplied by a negative number must behave the same way: multiplying a positive by a negative causes the negative to move backwards. So, if multiplying a positive by a negative moves it the “other way”, multiplying a negative by a negative must move the first number to the right.

It works, but it’s not as intuitive as I would have liked - I did better with why negative exponents are 1/x^n and why the angles in a triangle add up to 90 degrees.

[m11a]

The following page explains this one pretty well I think, skip to the "A proof" at the bottom: http://mathforum.org/dr.math/faq/faq.negxneg.html